37 research outputs found
Viscosity in the escape-rate formalism
We apply the escape-rate formalism to compute the shear viscosity in terms of
the chaotic properties of the underlying microscopic dynamics. A first passage
problem is set up for the escape of the Helfand moment associated with
viscosity out of an interval delimited by absorbing boundaries. At the
microscopic level of description, the absorbing boundaries generate a fractal
repeller. The fractal dimensions of this repeller are directly related to the
shear viscosity and the Lyapunov exponent, which allows us to compute its
values. We apply this method to the Bunimovich-Spohn minimal model of viscosity
which is composed of two hard disks in elastic collision on a torus. These
values are in excellent agreement with the values obtained by other methods
such as the Green-Kubo and Einstein-Helfand formulas.Comment: 16 pages, 16 figures (accepted in Phys. Rev. E; October 2003
A multibaker map for shear flow and viscous heating
A consistent description of shear flow and the accompanied viscous heating as
well the associated entropy balance is given in the framework of a
deterministic dynamical system. A laminar shear flow is modeled by a
Hamiltonian multibaker map which drives velocity and temperature fields. In an
appropriate macroscopic limit one recovers the Navier-Stokes and heat
conduction equations along with the associated entropy balance. This indicates
that results of nonequilibrium thermodynamics can be described by means of an
abstract, sufficiently chaotic and mixing dynamics. A thermostating algorithm
can also be incorporated into this framework.Comment: 11 pages; RevTex with multicol+graphicx packages; eps-figure
Role of chaos for the validity of statistical mechanics laws: diffusion and conduction
Several years after the pioneering work by Fermi Pasta and Ulam, fundamental
questions about the link between dynamical and statistical properties remain
still open in modern statistical mechanics. Particularly controversial is the
role of deterministic chaos for the validity and consistency of statistical
approaches. This contribution reexamines such a debated issue taking
inspiration from the problem of diffusion and heat conduction in deterministic
systems. Is microscopic chaos a necessary ingredient to observe such
macroscopic phenomena?Comment: Latex, 27 pages, 10 eps-figures. Proceedings of the Conference "FPU
50 years since" Rome 7-8 May 200